Abstract

Goos–Hänchen (GH) and Imbert–Fedorov (IF) shifts are diffractive corrections to geometric optics that have been extensively studied for a Gaussian beam that is reflected or transmitted by a dielectric interface. Propagating in free space before and after reflection or transmission, such a Gaussian beam spreads due to diffraction. We address here the question of how the GH and IF shifts behave for a “nondiffracting” Bessel beam.

© 2011 Optical Society of America

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References

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  1. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).
  2. F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
    [CrossRef]
  3. K. Artmann, Ann. Phys. 437, 87 (1948).
    [CrossRef]
  4. F. I. Fedorov, Dokl. Akad. Nauk SSSR 105, 465 (1955).
  5. C. Imbert, Phys. Rev. D 5, 787 (1972).
    [CrossRef]
  6. A. V. Novitsky and L. M. Barkovsky, J. Opt. A 10, 075006 (2008).
    [CrossRef]
  7. K. Yu. Bliokh and Yu. P. Bliokh, Phys. Rev. Lett. 96, 073903(2006).
    [CrossRef] [PubMed]
  8. K. Yu. Bliokh and Yu. P. Bliokh, Phys. Rev. E 75, 066609(2007).
    [CrossRef]
  9. A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437(2008).
    [CrossRef] [PubMed]
  10. M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
    [CrossRef] [PubMed]
  11. O. Hosten and P. Kwiat, Science 319, 787 (2008).
    [CrossRef] [PubMed]
  12. A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
    [CrossRef] [PubMed]
  13. M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photon. 3, 337 (2009).
    [CrossRef]
  14. V. G. Fedoseyev, J. Phys. A 41, 505202 (2008).
    [CrossRef]
  15. K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, Opt. Lett. 34, 389 (2009).
    [CrossRef] [PubMed]
  16. A. Aiello, M. Merano, and J. P. Woerdman, Opt. Lett. 34, 1207 (2009).
    [CrossRef] [PubMed]
  17. M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, Phys. Rev. A 82, 023817 (2010).
    [CrossRef]
  18. J. E. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
    [CrossRef]
  19. J. E. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  20. Y. Z. Umul, J. Opt. Soc. Am. A 27, 390 (2010).
    [CrossRef]
  21. G. S. McDonald, S. Chavez-Cerda, and G. H. C. New, Opt. Commun. 123, 225 (1996).
    [CrossRef]
  22. M. Santarsiero, R. Borghi, and M. A. Porras, J. Opt. Soc. Am. A 18, 1650 (2001).
    [CrossRef]
  23. J. Chen and Y. Yu., Opt. Commun. 283, 1655 (2010).
    [CrossRef]
  24. J. Arlt and K. Dholakia, Opt. Commun. 177, 297(2000).
    [CrossRef]
  25. A. Aiello and J. P. Woerdman, “Theory of angular Goos–Hänchen shift near Brewster incidence,” arXiv:0903.3730v2 (2009).
  26. The point here is rather subtle. The actual reason why we can predict the existence of an angular shift is because, in our calculations, we use the rigorous definition of a Dirac-delta distribution as a kind of limit of a sequence of regular functions (specifically, Gaussian functions). Conversely, a straightforward (and formally incorrect) symbolic manipulation of products of Dirac-delta singularities would lead to the absence of such a shift.
  27. A. Aiello and J. P. Woerdmanare preparing a manuscript to be called “Goos–Haenchen and Imbert–Fedorov shifts of an arbitrary paraxial beam.”

2010

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

J. Chen and Y. Yu., Opt. Commun. 283, 1655 (2010).
[CrossRef]

Y. Z. Umul, J. Opt. Soc. Am. A 27, 390 (2010).
[CrossRef]

2009

K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, Opt. Lett. 34, 389 (2009).
[CrossRef] [PubMed]

A. Aiello, M. Merano, and J. P. Woerdman, Opt. Lett. 34, 1207 (2009).
[CrossRef] [PubMed]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef] [PubMed]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photon. 3, 337 (2009).
[CrossRef]

2008

V. G. Fedoseyev, J. Phys. A 41, 505202 (2008).
[CrossRef]

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef] [PubMed]

A. V. Novitsky and L. M. Barkovsky, J. Opt. A 10, 075006 (2008).
[CrossRef]

A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437(2008).
[CrossRef] [PubMed]

2007

K. Yu. Bliokh and Yu. P. Bliokh, Phys. Rev. E 75, 066609(2007).
[CrossRef]

2006

K. Yu. Bliokh and Yu. P. Bliokh, Phys. Rev. Lett. 96, 073903(2006).
[CrossRef] [PubMed]

2004

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef] [PubMed]

2001

2000

J. Arlt and K. Dholakia, Opt. Commun. 177, 297(2000).
[CrossRef]

1996

G. S. McDonald, S. Chavez-Cerda, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[CrossRef]

1987

J. E. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

J. E. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

1972

C. Imbert, Phys. Rev. D 5, 787 (1972).
[CrossRef]

1955

F. I. Fedorov, Dokl. Akad. Nauk SSSR 105, 465 (1955).

1948

K. Artmann, Ann. Phys. 437, 87 (1948).
[CrossRef]

1947

F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

Aiello, A.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photon. 3, 337 (2009).
[CrossRef]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef] [PubMed]

A. Aiello, M. Merano, and J. P. Woerdman, Opt. Lett. 34, 1207 (2009).
[CrossRef] [PubMed]

A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437(2008).
[CrossRef] [PubMed]

A. Aiello and J. P. Woerdmanare preparing a manuscript to be called “Goos–Haenchen and Imbert–Fedorov shifts of an arbitrary paraxial beam.”

A. Aiello and J. P. Woerdman, “Theory of angular Goos–Hänchen shift near Brewster incidence,” arXiv:0903.3730v2 (2009).

Arlt, J.

J. Arlt and K. Dholakia, Opt. Commun. 177, 297(2000).
[CrossRef]

Artmann, K.

K. Artmann, Ann. Phys. 437, 87 (1948).
[CrossRef]

Barkovsky, L. M.

A. V. Novitsky and L. M. Barkovsky, J. Opt. A 10, 075006 (2008).
[CrossRef]

Bliokh, K. Y.

Bliokh, K. Yu.

K. Yu. Bliokh and Yu. P. Bliokh, Phys. Rev. E 75, 066609(2007).
[CrossRef]

K. Yu. Bliokh and Yu. P. Bliokh, Phys. Rev. Lett. 96, 073903(2006).
[CrossRef] [PubMed]

Bliokh, Yu. P.

K. Yu. Bliokh and Yu. P. Bliokh, Phys. Rev. E 75, 066609(2007).
[CrossRef]

K. Yu. Bliokh and Yu. P. Bliokh, Phys. Rev. Lett. 96, 073903(2006).
[CrossRef] [PubMed]

Borghi, R.

Chavez-Cerda, S.

G. S. McDonald, S. Chavez-Cerda, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[CrossRef]

Chen, J.

J. Chen and Y. Yu., Opt. Commun. 283, 1655 (2010).
[CrossRef]

Dholakia, K.

J. Arlt and K. Dholakia, Opt. Commun. 177, 297(2000).
[CrossRef]

Durnin, J. E.

J. E. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

J. E. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. E. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Fedorov, F. I.

F. I. Fedorov, Dokl. Akad. Nauk SSSR 105, 465 (1955).

Fedoseyev, V. G.

V. G. Fedoseyev, J. Phys. A 41, 505202 (2008).
[CrossRef]

Goos, F.

F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

Hänchen, H.

F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

Hermosa, N.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

Hosten, O.

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef] [PubMed]

Imbert, C.

C. Imbert, Phys. Rev. D 5, 787 (1972).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

Kivshar, Y. S.

Kwiat, P.

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef] [PubMed]

Leuchs, G.

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef] [PubMed]

Lindlein, N.

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef] [PubMed]

Marquardt, C.

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef] [PubMed]

McDonald, G. S.

G. S. McDonald, S. Chavez-Cerda, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[CrossRef]

Merano, M.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

A. Aiello, M. Merano, and J. P. Woerdman, Opt. Lett. 34, 1207 (2009).
[CrossRef] [PubMed]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photon. 3, 337 (2009).
[CrossRef]

Miceli, J. J.

J. E. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Murakami, S.

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef] [PubMed]

Nagaosa, N.

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef] [PubMed]

New, G. H. C.

G. S. McDonald, S. Chavez-Cerda, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[CrossRef]

Novitsky, A. V.

A. V. Novitsky and L. M. Barkovsky, J. Opt. A 10, 075006 (2008).
[CrossRef]

Onoda, M.

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef] [PubMed]

Porras, M. A.

Santarsiero, M.

Shadrivov, I. V.

Umul, Y. Z.

van Exter, M. P.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photon. 3, 337 (2009).
[CrossRef]

Woerdman, J. P.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photon. 3, 337 (2009).
[CrossRef]

A. Aiello, M. Merano, and J. P. Woerdman, Opt. Lett. 34, 1207 (2009).
[CrossRef] [PubMed]

A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437(2008).
[CrossRef] [PubMed]

A. Aiello and J. P. Woerdmanare preparing a manuscript to be called “Goos–Haenchen and Imbert–Fedorov shifts of an arbitrary paraxial beam.”

A. Aiello and J. P. Woerdman, “Theory of angular Goos–Hänchen shift near Brewster incidence,” arXiv:0903.3730v2 (2009).

Yu., Y.

J. Chen and Y. Yu., Opt. Commun. 283, 1655 (2010).
[CrossRef]

Ann. Phys.

F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

K. Artmann, Ann. Phys. 437, 87 (1948).
[CrossRef]

Dokl. Akad. Nauk SSSR

F. I. Fedorov, Dokl. Akad. Nauk SSSR 105, 465 (1955).

J. Opt. A

A. V. Novitsky and L. M. Barkovsky, J. Opt. A 10, 075006 (2008).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. A

V. G. Fedoseyev, J. Phys. A 41, 505202 (2008).
[CrossRef]

Nat. Photon.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photon. 3, 337 (2009).
[CrossRef]

Opt. Commun.

G. S. McDonald, S. Chavez-Cerda, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[CrossRef]

J. Chen and Y. Yu., Opt. Commun. 283, 1655 (2010).
[CrossRef]

J. Arlt and K. Dholakia, Opt. Commun. 177, 297(2000).
[CrossRef]

Opt. Lett.

Phys. Rev. A

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

Phys. Rev. D

C. Imbert, Phys. Rev. D 5, 787 (1972).
[CrossRef]

Phys. Rev. E

K. Yu. Bliokh and Yu. P. Bliokh, Phys. Rev. E 75, 066609(2007).
[CrossRef]

Phys. Rev. Lett.

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef] [PubMed]

K. Yu. Bliokh and Yu. P. Bliokh, Phys. Rev. Lett. 96, 073903(2006).
[CrossRef] [PubMed]

J. E. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef] [PubMed]

Science

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef] [PubMed]

Other

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

A. Aiello and J. P. Woerdman, “Theory of angular Goos–Hänchen shift near Brewster incidence,” arXiv:0903.3730v2 (2009).

The point here is rather subtle. The actual reason why we can predict the existence of an angular shift is because, in our calculations, we use the rigorous definition of a Dirac-delta distribution as a kind of limit of a sequence of regular functions (specifically, Gaussian functions). Conversely, a straightforward (and formally incorrect) symbolic manipulation of products of Dirac-delta singularities would lead to the absence of such a shift.

A. Aiello and J. P. Woerdmanare preparing a manuscript to be called “Goos–Haenchen and Imbert–Fedorov shifts of an arbitrary paraxial beam.”

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Equations (19)

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E ( R , φ , z ) = J m ( K 0 R ) e i m φ e i z k 0 2 - K 0 2 A ( R , φ ) e i z k 0 2 - K 0 2 ,
{ x = R cos φ , y = R sin φ .
K 0 = k 0 sin ϑ 0 , ( 0 ϑ 0 π / 2 ) .
sin ϑ 0 = K 0 / k 0 1.
J m ( K 0 R ) e i m φ = 1 2 π A ˜ ( k x , k y ) e i K · R d k x d k y ,
A ˜ ( k x , k y ) = A ˜ ( K , ϕ ) = 1 i m K 0 δ ( K K 0 ) e i m ϕ ,
A ˜ ( k x , k y ) A ˜ ( k x , k y ) = f ( K ) A ˜ ( k x , k y ) ,
X λ = i ln r λ θ = ϕ λ i R λ R λ ,
Y p = i f s f p ( 1 + r s r p ) cot θ , Y s = i f p f s ( 1 + r p r s ) cot θ ,
w p = a p 2 R p 2 a p 2 R p 2 + a s 2 R s 2 , w s = a s 2 R s 2 a p 2 R p 2 + a s 2 R s 2
Ξ = w p X p + w s X s , Ψ = w p Y p + w s Y s ,
Re ( Ξ ) = a p 2 R p 2 ϕ p + a s 2 R s 2 ϕ s a p 2 R p 2 + a s 2 R s 2 ,
Im ( Ξ ) = a p 2 R p R p + a s 2 R s R s a p 2 R p 2 + a s 2 R s 2 ,
Re ( Ψ ) = a p a s cot θ ( R p 2 + R s 2 ) sin η a p 2 R p 2 + a s 2 R s 2 a p a s cot θ [ 2 R p R s sin ( η ϕ p + ϕ s ) ] a p 2 R p 2 + a s 2 R s 2 ,
Im ( Ψ ) = a p a s cot θ ( R p 2 R s 2 ) cos η a p 2 R p 2 + a s 2 R s 2 .
k 0 Δ GH k 0 x r | z r = 0 = Re ( Ξ ) m Im ( Ψ ) ,
k 0 Δ IF k 0 y r | z r = 0 = Re ( Ψ ) + m Im ( Ξ ) ,
Θ GH x r z r = sin 2 ( ϑ 0 ) Im ( Ξ ) ,
Θ IF y r z r = sin 2 ( ϑ 0 ) Im ( Ψ ) ,

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